Ž. - Project Euclid
RANDOM WALK IN RANDOM ENVIRONMENT 1479 THEOREM B Deheuvels and Revesz 8Ž ´´.Ž.Ž.. Assuming 1.1 1.4,for any 0 and p 3, the following inequalities hold almost surely for all but finitely many n: Ž.log n 2 Ž.1.7 max S 2 k Ž.loglog n 0 k n Ž. Ž .Ž .1.8 log n log n Ž.Ž.log n 22log n22, 2 p 1 p where log j n denotes the jth iterative logarithmic function. a reflecting barrier at 0 ...